Technically, the Hilton - along with the other properties located in Hotel Plaza - actually is located on Disney property. Some years ago, it was also serviced by the same Disney bus transportation which today operates to/from Disney's own hotels.
Essentially, the difference is that the Swan and Dolphin largely function as Disney resorts (with a few notable exceptions), including Disney bus and boat transportation. The Hotel Plaza establishments - including the Hilton - operate more independently, and have their own (contracted) bus transportation to and from the parks.
Within Hotel Plaza, the Hilton offers access to EMH, which you should be able to use through the end of the day you check-out of the Hilton.